partialling

Partialling is a statistical technique used to isolate the relationship between two variables while controlling for the influence of one or more other variables. It is often employed in regression analysis and is closely related to the concept of partial correlation. The core idea is to remove the effect of a third variable (or set of variables) from the association between the two variables of interest.

Imagine you want to understand the relationship between ice cream sales and crime rates. You might observe a positive correlation. However, both might be influenced by a third variable: temperature. Higher temperatures lead to more ice cream sales and also tend to increase outdoor activity, potentially leading to more opportunities for crime. Partialling would involve removing the effect of temperature from both ice cream sales and crime rates, and then examining the remaining relationship between the two.

In practice, partialling is typically achieved through regression. For example, to partial out variable Z from the relationship between X and Y, one might first regress X onto Z and obtain the residuals (the part of X not explained by Z). Then, one would regress Y onto Z and obtain its residuals. Finally, the correlation between these two sets of residuals represents the partial correlation between X and Y, controlling for Z. This adjusted relationship provides a clearer picture of the direct association between the primary variables of interest, unconfounded by the control variable.